Our sky is immense. And some people across history have attempted - and partially succeeded- to regroup visible celestial objects into catalogues. Of particular interest are Charles Messier (1730-1817) and John Herschel (1792-1871).
Charles Messier created the catalog of Messier (M), listing 110 objects. It is widely used by amateur astronomers because the objects contained within are bright and easy to observe.
John Herschel completed the New General Catalogue of Nebulae and Clusters of Stars (NGC for New General Catalog), containing 7840 objects. The objects contained in this catalog are more difficult to observe for the most part. It is also mainly used by amateur astronomers in the southern hemisphere. A complement to this catalog was created (IC for Index Catalog).
There are a multitude of other more specific catalogs. When these objects are photographed in particular, their number in the catalog in question will be quoted. For example:
Barnard for dark nebulae
NDA. LBN, Vdb for reflection and dark nebulae
Sharpless for emission nebulae
Abell for clusters of massive galaxies